Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 10

Multiplication and Division, Part 2

Lesson 10

Math

Unit 3

3rd Grade

Lesson 10 of 23

Objective

Use the distributive property as a strategy to multiply by units of 7.

Common Core Standards

Core Standards

  • 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)
  • 3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Foundational Standards

  • 3.NBT.A.2
  • 3.OA.A.1
  • 3.OA.A.2

Criteria for Success

  1. Make use of structure by using the distributive property to decompose the 7 in a multiplication problem into 5 and 2 (or 1 and 6 or 3 and 4), multiplying those values separately by the other factor, then adding those products together to give the overall product (MP.7). 
  2. Look for structure by seeing the pattern between the 2s facts, the 5s facts, and the 7s facts (and optionally the 1s facts, 6s facts, and 7s facts, among others) and explain that pattern using the distributive property (MP.3, MP.7).
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Anchor Tasks

25-30 minutes

Problem 1

Identify all of the expressions below that are equivalent to $$7\times3$$.

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Guiding Questions

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Student Response

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Problem 2

a.   Solve.

  1.  

$$(8 \times 2) + (8 \times 5)$$

$$8\times(2+5)$$

$$8\times7$$
  1.  

$$(8\times6)+(8\times1)$$

$$8\times(6+1)$$

$$8\times7$$

b.   Use the reasoning in Part (a-i) to explain how you could use $$3\times5$$ to solve $$3\times7$$.

c.   Use the reasoning in Part (a-ii) to explain how you could use $$5\times6$$ to solve $$5\times7$$.

Guiding Questions

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Student Response

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Problem 3

Decompose 7 into a sum of two addends in the following expression and use those values to find the following products. 

$$6\times7$$

Guiding Questions

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Student Response

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Problem 4

Explain how the relationship we just explored is shown on the multiplication table below.

× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56     80
9 9 18 27 36 45 54 63     90
10 10 20 30 40 50 60 70 80 90 100

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • What is the value of the three expressions in #1? What does that mean in terms of their relationship to one another? 
  • Which option did you choose for #2? How did you know the others were incorrect? 
  • Which option did you choose for #4? How did you know the others were incorrect? 
  • Which equations were true in #5? How do you know? 
  • How did you decompose the 7 in #6? Could you have decomposed the other factor? Why?
  • Who is correct in #7? How did Malia solve? How did Leonidas solve? Why is it possible to solve in both ways?
  • How can decomposing 7 into a sum of two addends help to solve multiplication problems involving 7?

Target Task

5-10 minutes

The array below shows how $$7\times3$$ can be decomposed into two parts to make the computation easier. Use the array to fill in the blanks in the equations below.

$$\begin{align} {\bf(7\times3)} &=\left(5\times3\right)+\left( \underline{\ \ \ \ } \times \underline{\ \ \ \ } \right) \\ &= \underline{\ \ \ \ \ \ \ \ \ \ \ \ }\ +\ \underline{\ \ \ \ \ \ \ \ \ \ \ \ } \\ &=\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ } \end{align}$$

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Solve one- and two-step word problems involving units up to 7.

Lesson 11
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to The Properties of Operations

Topic B: Multiplication and Division by 6 and 7

Topic C: Multiplication and Division by 8 and 9

Topic D: Multiplication and Division by Values Greater than 10

Topic E: Two-Step Word Problems and Patterns in Arithmetic

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